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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Calibration of Heston's Model on SPX data\n",
      "=======================================\n",
      "\n",
      "This notebook demonstrates the calibration of Heston's model on SPX data, using the QuantLib *HestonModel* class. \n",
      "The code is adapted from the test suite written by Klaus Spandersen.\n",
      "\n",
      "The calibration function takes as input a `pandas.DataFrame` constructed in notebook OptionQuotes.\n",
      "\n",
      "QuantLib dependencies\n",
      "---------------------"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import pandas\n",
      "from pandas import DataFrame\n",
      "import datetime\n",
      "\n",
      "from quantlib.models.equity.heston_model import (\n",
      "    HestonModelHelper, HestonModel)\n",
      "from quantlib.models.calibration_helper import ImpliedVolError\n",
      "from quantlib.processes.heston_process import HestonProcess\n",
      "from quantlib.pricingengines.api import AnalyticHestonEngine\n",
      "from quantlib.math.optimization import LevenbergMarquardt, EndCriteria\n",
      "from quantlib.settings import Settings\n",
      "from quantlib.time.api import Period, Date, Actual365Fixed, TARGET, Days\n",
      "from quantlib.quotes import SimpleQuote\n",
      "from quantlib.termstructures.yields.zero_curve import ZeroCurve\n",
      "\n",
      "from quantlib.util.converter import pydate_to_qldate, df_to_zero_curve\n",
      "import quantlib.reference.names as nm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Utility functions\n",
      "-----------------\n",
      "\n",
      "The calibration process uses some utility functions, defined below.\n",
      "The main task is to convert the data into a set of helper objects, one per data point (bid and ask prices)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def heston_helpers(df_option, df_rates):\n",
      "    \"\"\"\n",
      "    Create array of heston options helpers\n",
      "    \"\"\"\n",
      "\n",
      "    trade_date = df_option[nm.TRADE_DATE].ix[0]\n",
      "    settlement_date = pydate_to_qldate(trade_date)\n",
      "    \n",
      "    settings = Settings()\n",
      "    settings.evaluation_date = settlement_date\n",
      "\n",
      "    calendar = TARGET()\n",
      "\n",
      "    # convert data frame (date/value) into zero curve\n",
      "    # expect the index to be a date, and 1 column of values\n",
      "\n",
      "    risk_free_ts = df_to_zero_curve(df_rates['iRate'], trade_date)\n",
      "    dividend_ts = df_to_zero_curve(df_rates[nm.DIVIDEND_YIELD], trade_date)\n",
      "\n",
      "    # loop through rows in option data frame, construct\n",
      "    # helpers for bid/ask\n",
      "\n",
      "    \n",
      "    options = []\n",
      "    for index, row in df_option.T.iteritems():\n",
      "\n",
      "        strike = row[nm.STRIKE]\n",
      "        spot = row[nm.SPOT]\n",
      "        if (strike/spot > 1.3) | (strike/spot < .7):\n",
      "            continue\n",
      "        \n",
      "        expiry_date = row[nm.EXPIRY_DATE]\n",
      "        \n",
      "        days = (expiry_date - trade_date).days\n",
      "        maturity = Period(days, Days)\n",
      "\n",
      "        options.append(\n",
      "                HestonModelHelper(\n",
      "                    maturity, calendar, spot,\n",
      "                    strike, SimpleQuote(row['IVBid']),\n",
      "                    risk_free_ts, dividend_ts,\n",
      "                    ImpliedVolError))\n",
      "        \n",
      "        options.append(\n",
      "                HestonModelHelper(\n",
      "                    maturity, calendar, spot,\n",
      "                    strike, SimpleQuote(row['IVAsk']),\n",
      "                    risk_free_ts, dividend_ts,\n",
      "                    ImpliedVolError))\n",
      "\n",
      "    return {'options':options, 'spot': spot}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The function merge_df merges the result of the calibration (fitted option price and fitted implied volatility)\n",
      "with the input data set. This will facilitate the plotting of actual vs. fitted volatility."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def merge_df(df_option, options, model_name):\n",
      "    df_output = DataFrame.filter(df_option,\n",
      "                items=['dtTrade', 'dtExpiry',\n",
      "                       'Type', 'Strike', 'Mid',\n",
      "                       'QuickDelta', 'IVBid', 'IVAsk',\n",
      "                       'iRate', 'dRate', 'ATMVol', 'Fwd'])\n",
      "\n",
      "    model_value = np.zeros(len(df_option))\n",
      "    model_iv = np.zeros(len(df_option))\n",
      "    for i, j in zip(range(len(df_option)), range(0, len(options),2)):\n",
      "        model_value[i] = options[j].model_value()\n",
      "        model_iv[i] = options[j].impliedVolatility(model_value[i],\n",
      "            accuracy=1.e-5, maxEvaluations=5000,\n",
      "            minVol=.01, maxVol=10.0)\n",
      "\n",
      "    df_output[model_name + '-Value'] = model_value\n",
      "    df_output[model_name + '-IV'] = model_iv\n",
      "    \n",
      "    return df_output"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The calibration process\n",
      "-----------------------\n",
      "\n",
      "The calibration process is performed by the following function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def heston_calibration(df_option, ival=None):\n",
      "    \"\"\"\n",
      "    calibrate heston model\n",
      "    \"\"\"\n",
      "\n",
      "    # extract rates and div yields from the data set    \n",
      "    df_tmp = DataFrame.filter(df_option, items=['dtExpiry', 'iRate', nm.DIVIDEND_YIELD])\n",
      "    \n",
      "    grouped = df_tmp.groupby('dtExpiry')\n",
      "    \n",
      "    def aggregate(serie):\n",
      "        return serie[serie.index[0]]\n",
      "    \n",
      "    df_rates = grouped.agg(aggregate)\n",
      "    \n",
      "    trade_date = df_option[nm.TRADE_DATE][0]\n",
      "    expiry_date = df_option[nm.EXPIRY_DATE][0]\n",
      "    \n",
      "    spot = df_option[nm.SPOT][0]\n",
      "    \n",
      "    # build array of option helpers\n",
      "    hh = heston_helpers(df_option, df_rates)\n",
      "    options = hh['options']\n",
      "    spot = hh['spot']\n",
      "\n",
      "    risk_free_ts = df_to_zero_curve(df_rates[nm.INTEREST_RATE], trade_date)\n",
      "    dividend_ts = df_to_zero_curve(df_rates[nm.DIVIDEND_YIELD], trade_date)\n",
      "\n",
      "    # initial values for parameters\n",
      "    if ival is None:\n",
      "        ival = {'v0': 0.1, 'kappa': 1.0, 'theta': 0.1,\n",
      "        'sigma': 0.5, 'rho': -.5}\n",
      "\n",
      "    process = HestonProcess(\n",
      "        risk_free_ts, dividend_ts, SimpleQuote(spot), ival['v0'], ival['kappa'],\n",
      "         ival['theta'], ival['sigma'], ival['rho'])\n",
      "\n",
      "    model = HestonModel(process)\n",
      "    engine = AnalyticHestonEngine(model, 64)\n",
      "\n",
      "    for option in options:\n",
      "        option.set_pricing_engine(engine)\n",
      "\n",
      "    om = LevenbergMarquardt(1e-8, 1e-8, 1e-8)\n",
      "    model.calibrate(\n",
      "        options, om, EndCriteria(400, 40, 1.0e-8, 1.0e-8, 1.0e-8)\n",
      "    )\n",
      "\n",
      "    print('model calibration results:')\n",
      "    print('v0: %f kappa: %f theta: %f sigma: %f rho: %f' %\n",
      "          (model.v0, model.kappa, model.theta, model.sigma,\n",
      "           model.rho))\n",
      "\n",
      "    calib_error = (1.0/len(options)) * sum(\n",
      "        [pow(o.calibration_error()*100.0,2) for o in options])\n",
      "\n",
      "    print('SSE: %f' % calib_error)\n",
      "\n",
      "    # merge the fitted volatility and the input data set\n",
      "    return merge_df(df_option, options, 'Heston')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Calibration\n",
      "-----------\n",
      "\n",
      "Finally, the calibration is performed by first loading the option data and calling the calibration routine.\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "df_options = pandas.read_pickle('df_options_SPX_24jan2011.pkl')\n",
      "df_heston_cal = heston_calibration(df_options)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "model calibration results:\n",
        "v0: 0.051965 kappa: 0.977303 theta: 0.102573 sigma: 0.987787 rho: -0.747035\n",
        "SSE: 0.935261\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot Actual vs. Fitted Implied Volatility\n",
      "-----------------------------------------\n",
      "\n",
      "We display 4 graphs in one plot, and show the bid/ask market volatility with the fitted volatility\n",
      "for selected maturities."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def calibration_subplot(ax, group, i, model_name):\n",
      "    group = group.sort_index(by='Strike')\n",
      "    dtExpiry = group.get_value(group.index[0], 'dtExpiry')\n",
      "    K = group['Strike']\n",
      "    VB = group['IVBid']\n",
      "    VA = group['IVAsk']\n",
      "    VM = group[model_name + '-IV']\n",
      "\n",
      "    ax.plot(K, VA, 'b.', K,VB,'b.', K,VM,'r-')\n",
      "    if i==3:\n",
      "        ax.set_xlabel('Strike')\n",
      "    if i==0:\n",
      "        ax.set_ylabel('Implied Vol')\n",
      "    ax.text(.6,.8,'%s' % dtExpiry, transform=ax.transAxes)\n",
      "    \n",
      "def calibration_plot(title, df_calibration, model_name):\n",
      "    df_calibration = DataFrame.filter(df_calibration,\n",
      "                    items=['dtExpiry', \n",
      "                           'Strike', 'IVBid', 'IVAsk',\n",
      "                           'TTM', model_name+'-IV'])\n",
      "\n",
      "    # group by maturity\n",
      "    grouped = df_calibration.groupby('dtExpiry')\n",
      "\n",
      "    all_groups = [(dt, g) for dt, g in grouped]\n",
      "    \n",
      "    xy = [(0,0), (0,1), (1,0), (1,1)]\n",
      "\n",
      "    for k in range(0, len(all_groups),4):\n",
      "        if (k+4) >= len(all_groups):\n",
      "            break\n",
      "        plt.figure()\n",
      "        fig, axs = plt.subplots(2, 2, sharex=True, sharey=True)\n",
      "\n",
      "        for i in range(4):\n",
      "            x,y = xy[i]\n",
      "            calibration_subplot(axs[x,y], all_groups[i+k][1],i, model_name)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dtTrade = df_options['dtTrade'][0]\n",
      "title = 'Heston Model (%s)' % dtTrade\n",
      "calibration_plot(title, df_heston_cal, 'Heston')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x4605d90>"
       ]
      },
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AqN6DlUx6em8bXcbOTpjBdegQsHu3sAnWM4liDb6HBahys/RTp05h3bp1SExM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\nCGOMMb39P5uQ/i1woEtjAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4624550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x46bbb50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bgDdDiyrl+2B/CWMK2NgAO3bVRJ3Z04C0NCAhQVjO/f130dpQ90BljtFcFe4T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\nYRiG0Zn/BxjrdpbjWBkUAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4a4a310>"
       ]
      }
     ],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}
